Finite Group Databasebeta

← #23765764

Subgroups — #23765764

Order 10112.

628 conjugacy classes of subgroups; only the 325 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic158C211yesmaximal, characteristic
2C2×#14579126C212yesmaximal
3C4⋊C4×Dic79C212yesmaximal
4C4×Dic79⋊C4C214yesmaximal
5#19098414C212yesmaximal
6#19098409C211yesmaximal, characteristic
7#19098408C212yesmaximal
8C4×C4⋊C4×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10C4×Dic158C418yescomplemented
11#14579126C4116yescomplemented
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4C2214yes—
14C2×Dic79⋊C4C2212yes—
15C2×C4×Dic79C2214yes—
16C2×C4×Dic79C2212yes—
17C2×C4×Dic79C2214yes—
18C2×C4×Dic79C2212yes—
19C79⋊#95C2211yescharacteristic
20C79⋊#95C2214yes—
21C79⋊#95C2211yescharacteristic
22C79⋊#95C2212yes—
23C2×C4⋊C4×C79C2212yes—
24C2×C42×C79C2212yes—
25C2×C42×C79C2211yescharacteristic
26#95×C79C2212yes—
27C2×Dic158C2×C418yes—
28C2×Dic158C2×C414yes—
29C22×Dic79C2312yes—
30C22×Dic79C2312yes—
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C4⋊Dic79C2×C414yes—
34Dic79⋊C4C2×C4116yes—
35Dic79⋊C4C2×C418yes—
36C4×Dic79—44no—
37C4×Dic79C2×C4116yes—
38C4×Dic79C2×C418yes—
39C4×Dic79C2×C418yes—
40C22×C4×C79C2311yescharacteristic
41C22×C4×C79C2314yes—
42C22×C4×C79C2311yescharacteristic
43C22×C4×C79C2311yescharacteristic
44C4⋊C4×C79C2×C418yes—
45C42×C79—42no—
46C42×C79C2×C414yes—
47C23×C79C2411yescharacteristic
48C2×C4×C79—24no—
49C2×C4×C79—21no—
50C2×C4×C79—22no—
51C2×C4×C79—24no—
52C2×C4×C79—21no—
53C2×C4×C79C22×C412yes—
54C2×C4×C79C22×C418yes—
55C2×C4×C79C22×C412yes—
56C2×C4×C79C22×C414yes—
57C2×C4×C79C22×C412yes—
58C2×Dic79—22no—
59C2×Dic79—22no—
60C2×Dic79—22no—
61C2×Dic79—22no—
62C2×Dic79—22no—
63C2×Dic79—22no—
64C2×Dic79C22×C414yes—
65C2×Dic79C22×C414yes—
66C2×Dic79C22×C414yes—
67C2×Dic79C22×C418yes—
68C2×Dic79C22×C414yes—
69Dic158C42116yescomplemented
70C22×C79C23×C412yes—
71C22×C79C23×C411yescharacteristic
72C22×C79H(5,𝔽2)11yescharacteristic
73C22×C792−1+412yes—
74C22×C792−1+411yescharacteristic
75C4×C79—22no—
76C4×C79—28no—
77C4×C79—22no—
78C4×C79C2×C4214yes—
79Dic79—24no—
80Dic79—24no—
81Dic79—24no—
82Dic79C2×C4218yes—
83C2×C79C22×C4211yescharacteristic
84C2×C79#51912yes—
85C2×C79#51911yescharacteristic
86C2×C79#52012yes—
87C2×C79#52011yescharacteristic
88#2276—791nomaximal, Sylow
89C79#227611yescharacteristic, complemented, Sylow
90C2×C4×Q8—792no—
91C2×C4×Q8—791no—
92C4×C4⋊C4—792no—
93C4×C4⋊C4—794no—
94C4×C4⋊C4—792no—
95C4×C4⋊C4D7911yescharacteristic
96#376—791no—
97#376—792no—
98C22×Q8—791no—
99C4×Q8—7916no—
100C4×Q8—798no—
101C2×C4⋊C4—792no—
102C2×C4⋊C4—794no—
103C2×C4⋊C4—791no—
104C2×C4⋊C4C2×D7912yes—
105C2×C42—794no—
106C2×C42—794no—
107C2×C42—792no—
108C2×C42—792no—
109C2×C42C2×D7912yes—
110C2×C42C2×D7911yescharacteristic
111#95—791no—
112#95—792no—
113#95—794no—
114#95—791no—
115#95C2×D7912yes—
116C2×Q8—798no—
117C2×Q8—794no—
118C22×C4—792no—
119C22×C4—792no—
120C22×C4—792no—
121C22×C4—792no—
122C22×C4C22×D7911yescharacteristic
123C22×C4C22×D7911yescharacteristic
124C22×C4C22×D7914yes—
125C22×C4C22×D7911yescharacteristic
126C4⋊C4—7916no—
127C4⋊C4—798no—
128C4⋊C4—794no—
129C4⋊C4C4×D7918yes—
130C42—42no—
131C42—3164no—
132C42—7916no—
133C42—798no—
134C42—798no—
135C42C4×D7914yes—
136C23C23×D7911yescharacteristic
137Q8—7916no—
138C2×C4—21no—
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—24no—
142C2×C4—21no—
143C2×C4—798no—
144C2×C4—794no—
145C2×C4—794no—
146C2×C4—794no—
147C2×C4—794no—
148C2×C4—1582no—
149C2×C4—1582no—
150C2×C4—1582no—
151C2×C4—1582no—
152C2×C4—1582no—
153C2×C4—1582no—
154C2×C4C2×C4×D7912yes—
155C2×C4C2×C4×D7918yes—
156C2×C4C2×C4×D7912yes—
157C2×C4C2×C4×D7914yes—
158C2×C4C2×C4×D7912yes—
159C22C22×C4×D7912yes—
160C22C22×C4×D7911yescharacteristic
161C22#1457920611yescharacteristic
162C22#1457920812yes—
163C22#1457920911yescharacteristic
164C4—22no—
165C4—28no—
166C4—22no—
167C4—798no—
168C4—1584no—
169C4—1584no—
170C4—1584no—
171C4C42×D7914yes—
172C2C2×C42×D7911yescharacteristic
173C2#1909903912yes—
174C2#1909904011yescharacteristic
175C2#1909904212yes—
176C2#1909904411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC2×C79C22×C42
FittingC4×C4⋊C4×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC4×C4⋊C4D79
hypocenterC79#2276
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. C4×Dic158C4semidirect
11. #14579126C4semidirect
69. Dic158C42semidirect
89. C79#2276semidirect